Depletion-limited Kerr solitons in singly resonant optical parametric oscillators

We analyze the impact of pump depletion in the generation of parametrically driven Kerr cavity solitons in a degenerate optical parametric oscillator. Using variational methods, we derive an analytical expression that describes the soliton existence region. We use this expression to study the energy conversion efficiency and compare it to a linearly driven Kerr resonator modeled by the Lugiato-Lefever equation. Parametric driving is more efficient at high walk-off between the continuous wave driving and the soliton.